Question

wnloads/HW5 pdf Create a MATLAB code to calculate function f (z) = ei8r at any given point using Taylor series. Write a script file called myTaylor.m and a function file called myFact.m to do the following: (a) The function myFact.m should return the factorial of a number when sent the number. In the script file: i. Set the starting point as r0-1 and fo = f(d)-6.049647 ii. Ask the user to enter his/her desired point and store it in x1 iii. Calculate the true solution for f(r1) and store it in TrueF1 iv. Calculate the first term of Taylor series at x1 and store it in TaylorF1 v. Calculate the true relative error of TaylorF1 and store it in TrueError vi. Use while loop and calculate next terms of Taylor formulation until the true relative error is less than 2%. (b) Once the next term is calculated, it should be added to the current value of TaylorF1 and the TrueError should be updated. i. Print the values of TaylorF1 and TrueError after each calculation ii. Count the number of Taylor formulation terms and print them (c) Run your program twice i. For x1 1.13 (you tan compare the results of this case with Question 2 ii. For one other x1 value of your choice. -IMG 6938JPG AIMG 6937 PG 4 5 6 8

Answer 1

Define a function in a file named average.m that accepts an input vector, calculates the average of the values, and returns a single result.

function y = average(x)
if ~isvector(x)
    error('Input must be a vector')
end
y = sum(x)/length(x); 
end

Call the function from the command line.

z = 1:99;
average(z)

ans =
    50

Function in a Script File

Try it in MATLAB

Define a script in a file named integrationScript.m that computes the value of the integrand at
2m/3
and computes the area under the curve from 0 to . Include a local function that defines the integrand,
y sin(z)
.

Note: Including functions in scripts requires MATLAB® R2016b or later.

% Compute the value of the integrand at 2*pi/3.
x = 2*pi/3;
y = myIntegrand(x)

% Compute the area under the curve from 0 to pi.
xmin = 0;
xmax = pi;
f = @myIntegrand;
a = integral(f,xmin,xmax)

function y = myIntegrand(x)
y = sin(x).^3;
end

y =

    0.6495


a =

    1.3333

Function with Multiple Outputs

Define a function in a file named stat.m that returns the mean and standard deviation of an input vector.

function [m,s] = stat(x)
n = length(x);
m = sum(x)/n;
s = sqrt(sum((x-m).^2/n));
end

Call the function from the command line.

values = [12.7, 45.4, 98.9, 26.6, 53.1];
[ave,stdev] = stat(values)

ave =
   47.3400
stdev =
   29.4124

Multiple Functions in a Function File

Define two functions in a file named stat2.m, where the first function calls the second.

function [m,s] = stat2(x)
n = length(x);
m = avg(x,n);
s = sqrt(sum((x-m).^2/n));
end

function m = avg(x,n)
m = sum(x)/n;
end

Function avg is a local function. Local functions are only available to other functions within the same file.

Call function stat2 from the command line.

values = [12.7, 45.4, 98.9, 26.6, 53.1];
[ave,stdev] = stat2(values)

ave =
   47.3400
stdev =
   29.4124